I know most red lasers use much more current than a blu-ray. But thats about it. You may need to re-phrase the question because I, for one, don't fully understand.
You mean a regular old 5 mW diode as used in cheap pointers? It seems to vary among units, but i've measured them around 20 mA. You should be careful though, the range between treshold and destructive current is rather narrow in these little things.
You should probably have an adjustable current source though, just ramp it up to the threshold and be very careful from there on. These things have specifications like nominal power 5 mW, absolute maximum 7 mW, and they will actually break quickly at maximum power too.
I'm wondering because i have a flash light which uses a aa battery and boosts the volts to 4.5 and it can power a cheap red.It may be good for a blu-ray